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Title: On the Semi-absoluteness of Isomorphisms between the Pro-$p$ Arithmetic Fundamental Groups of Smooth Varieties
Authors: Tsujimura, Shota
Author's alias: 辻村, 昇太
Keywords: 14H30
Anabelian geometry
étale fundamental group
hyperbolic curve
configuration space
p-adic local field
pro-p Grothendieck conjecture
Issue Date: 11-Oct-2023
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Journal title: Publications of the Research Institute for Mathematical Sciences
Volume: 59
Issue: 3
Start page: 507
End page: 541
Abstract: Let p be a prime number. In the present paper, we consider a certain pro-p analogue of the semi-absoluteness of isomorphisms between the étale fundamental groups of smooth varieties over p-adic local fields [i.e., finite extensions of the field of p-adic numbers ℚp​] obtained by Mochizuki. This research was motivated by Higashiyama’s recent work on the pro-p analogue of the semi-absolute version of the Grothendieck conjecture for configuration spaces [of dimension ≥2] associated to hyperbolic curves over generalized sub-p-adic fields [i.e., subfields of finitely generated extensions of the completion of the maximal unramified extension of ℚp​].
Rights: © 2023 Research Institute for Mathematical Sciences, Kyoto University.
This work is licensed under a CC BY 4.0 license.
DOI(Published Version): 10.4171/prims/59-3-3
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